Question

Find the area of the iscoseles triangle first answer=brainliest

Answer 1

Answer:

$60cm^{2}$

Step-by-step explanation:

so first we need to find the height so by splitting the isosceles triangle into two right-angled triangles and then applying Pythagoras' Theorem to one of them.

$h^{2} =13^{2} -5^{2}$

$h^{2} =169-25$

$h^{2} =144$

$h=\sqrt{144}$

$h=12$

We now know the height of the triangle and can use this to go back and find the area of the isosceles triangle.

area of triangle = $\frac{1}{2}$ x base x height

area of triangle = $\frac{1}{2}$ x 10 x 12

area of triangle = 60

Answer 2

Answer:

$\boxed{Area = 60 cm^2}$

Step-by-step explanation:

Perimeter of the isosceles triangle = 10+13+13

=> 36 cm

Semi Perimeter = 18 cm

Using Heron's formula to find the area:

=> $Area = \sqrt{s(s-a)(s-b)(s-c)}$

Where s is the semi perimeter and a,b and c are the sides

=> Area = $\sqrt{18(18-13)(18-13)(18-10) }$

=> Area = $\sqrt{18(5)(5)(8)}$

=> Area = $\sqrt{3600}$

=> Area = 60 cm²